Why does this code work?

Question

double squareRoot(double num) {
double low = 1.0;
double high = num;
for (int i = 0; i < 30; i = i + 1) {
double estimate = (high + low) / 2;
if (estimate*estimate > num) {
double newHigh = estimate;
high = newHigh;
} else {
double newLow = estimate;
low = newLow;
}
}
return (high + low) / 2;
}
int main () {
cout << squareRoot(9); //Enter the number that you want to take square root of.
}

Answer 1

Don't all programmers ask that question : "why does this code work?"

Answer 2

is it working or not working ! ..?

Answer 3

It is working but I don't understand why it works. If you plug the number you want to take square root of, it operates sucessfully. So I was wondering if someone could explain the code